Mayor Bill de Blasio swept to victory last year with a promise to salve the wounds of New Yorkers who distrusted the police. His critics warned that crime would soar again.

So far, neither has happened.

Now, as protests over the Eric Garner case course through New York City and beyond, Mr. de Blasio’s pledge to bridge the police-community divide has become, with escalating urgency, perhaps the foremost challenge of his mayoralty. It is a cause with an audience from Ferguson, Mo., to Capitol Hill to the city police precincts, where some rank-and-file officers remain wary of the mayor’s calls for reform.

On Thursday, he outlined a series of planned changes in police training, a day after a Staten Island grand jury declined to indict a white police officer who in July performed a chokehold on Mr. Garner, an unarmed black man who died after the confrontation.

The police will be taught strategies to control ego and adrenaline and urged to suppress profanity, city officials said. Officers will be exposed to the culture of the communities they are asked to patrol and given new guidance on how to persuade suspects to comply with arrest without the use of force.

“People need to know that black lives and brown lives matter as much as white lives,” Mr. de Blasio said at the new Police Academy in Queens.

“We are all responsible now,” he added. “The weight of history can’t be our excuse.”

The Garner episode has forced Mr. de Blasio, a Democrat, atop a tightrope of sorts — balancing sympathy for protesters with support for the officers in charge of keeping the city safe.

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Excerpts from Bill de Blasio’s speeches on race, inequality, community courts and policing during his years campaigning for public office, and while serving as mayor of New York.Published OnDec. 4, 2014CreditImage by Chang W. Lee/The New York Times

As the case laid bare even before the grand jury’s decision, the relationship between the police and many of those they serve remains as fraught as ever.

On the heels of the protests in Ferguson, where another white officer was cleared by a grand jury after a fatal encounter with an unarmed black man, community leaders in New York and elsewhere have professed a flagging faith in the justice system.

Others have chafed at the pace of change under Mr. de Blasio and questioned whether his proposals, like a pilot program to place body cameras on officers and a less stringent marijuana policy, would prove sufficient.

With the mayor’s blessing, officers continue to pursue low-level crime aggressively as part of a “broken windows” strategy long championed by Police Commissioner William J. Bratton. Mr. Garner had been accused of selling loose cigarettes, a subject of community complaints

“I feel for the mayor; he’s in a bind,” Councilman Ritchie Torres of the Bronx said. “On the ground, I’m sensing a level of anger and a level of suspicion toward the N.Y.P.D. that I’ve never seen before.”

Mr. de Blasio has spoken passionately of the pain wrought by the Garner case, repeatedly invoking his son, Dante, who is biracial, when describing his reaction. But he has not explicitly denounced the grand jury decision, as fellow elected officials have.

In an effort to trumpet accomplishments on police issues, the mayor moved up a series of events this week, including an announcement about reduced crime rates, to coincide with the Garner decision.

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Mayor Bill de Blasio said it was necessary and important to change the way communities are policed in New York and the rest of the country.Published OnDec. 4, 2014CreditImage by Todd Heisler/The New York Times

While many lawmakers have welcomed the changes announced so far, and have acknowledged that cultural shifts at the department will take time, Mr. Garner’s example has inspired pitched calls for more immediate action.

“Retraining is nothing to sneeze at,” Councilman Jumaane D. Williams of Brooklyn said. “I think the frustration is, what can we do today?”

Mr. Williams has also been critical of the police over the death last month of Akai Gurley, an unarmed black man shot by an officer patrolling a public housing staircase in Brooklyn with his gun drawn. Mr. Williams, as well as civil rights leaders, have tied that shooting to Mr. Garner’s death as twin examples of a disregard for the lives of black men.

The episodes have intensified the spotlight on the most scrutinized relationship in city government: that of the mayor and his police commissioner.

In many ways, Mr. Bratton’s return to New York, after serving in the job under Mayor Rudolph W. Giuliani, a Republican, has been a sharp departure from his tenure in the 1990s.

At his introductory news conference, he displayed a 1956 children’s book, “Your Police,” intended to signal a gentler approach. He has held aloft a bag of oregano to demonstrate how much marijuana New Yorkers could carry while remaining eligible for a mere summons. In a speech in October, Mr. Bratton vowed to rid the department of “the brutal, the corrupt, the racist, the incompetent.”

On the night of the grand jury decision in Ferguson, Mr. Bratton headed to Times Square where demonstrators gathered, close enough that one protester doused him and several other officers with fake blood.

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The president of the Patrolmen’s Benevolent Association, Patrick J. Lynch, said Mayor Bill de Blasio’s comments on the Eric Garner case were unfair to police officers.Published OnDec. 4, 2014CreditImage by Yana Paskova for The New York Times

On Wednesday night, he spent about two hours at a Police Headquarters command center, watching images of protests around the city.

While Mr. Bratton’s reputation has afforded Mr. de Blasio a measure of cover with law enforcement, many officers remain skeptical of the mayor’s designs.

Patrick J. Lynch, the head of the patrolman’s union, said on Thursday that Mr. de Blasio had thrown police officers “under the bus” in his remarks after the grand jury decision.

Others have been more measured. Roy T. Richter, the president of the Captains Endowment Association, which represents the Police Department’s upper echelon, said the police and the mayor deserved credit for managing the protests on Wednesday night. But he echoed a sense of embattlement expressed by many officers in recent days.

“Yesterday I was in the car with my 10-year-old listening to a group of congressmen at a press conference and then the president of the United States talking about policing in a way that was very negative,” Mr. Richter said. “It was not a good feeling.”

City officials affirmed on Thursday that an internal police investigation, as well as a federal inquiry, were active.

Mr. Torres, the co-sponsor of a bill requiring officers to identify themselves during exchanges with civilians and to give a reason for the encounters, said the department’s continued focus on low-level crime suggested “post-traumatic stress from the 1990s.”

Thomas A. Reppetto, a historian of the New York City police and the former president of the city’s Citizen’s Crime Commission, likened the adherence to the “broken windows” model to an outmoded military strategy. “The Police Department is ready to fight the last war because that’s the one they won,” he said. “That’s the one they know well.”

Al Baker contributed reporting.

A version of this article appears in print on , on Page A1 of the New York edition with the headline: Mayor Striving to Back Police and Protesters. Order Reprints | Today’s Paper | Subscribe